1. Field of the Invention
This invention relates to the field of filters for stochastic processes, and more specifically, to stress test systems and reducing baseline noise in electrocardiographic (ECG) signals by filtering techniques.
2. Description of the Prior Art
Random, or stochastic, noise is a problem that exists in many electrical and electronic signals. Distortion within the baseline of an ECG signal caused by such random noise is an existing problem in analyzing electrocardiograms. Numerous publications have dealt with the low frequency cutoff requirements of ECG signals. Recent recommendations of Ad Hoc Writing Group of the Committee on Electrocardiography and Cardiac Electrophysiology of the Council on Clinical Cardiology of the American Heart Association states that the low frequency cutoff should be on the order of 0.67 Hz provided that the filter meets certain phase and amplitude requirements.
Various techniques have been employed to reduce base line distortion in electrocardiographic (ECG) signals. The most common technique presently used is Cubic-Spline interpolation where the onset of QRS signals are isolated and interpolation techniques are employed to determine the smoothest curve joining several QRS onsets. The ECG baseline can then be estimated by subtracting the curve representing the baseline wander as estimated by the Cubic-Spline technique from the recorded ECG signal. However, the QRS onset points used by the Cubic-Spline method, do not sufficiently model noise in an ECG baseline due to the scarcity of interpolation points at low heart rates. Determination of the QRS onset can be difficult or impossible in the presence of high amplitude baseline wander. Furthermore, it is necessary to delay the ECG in order to obtain reference points (QRS onset points) for calculation of the cubic spine curve. This delay (often as long as 5 seconds or longer) renders the cubic spline interpolation unsuitable for real time monitoring of patients.
A faster method of correcting baseline distortion has been to use high pass filtering techniques. One such filtering technique is to employ Finite Impulse Response (FIR) filters, where the output is taken after the FIR transfer is combined with a delay based on an integral number of the filter. These filters offer a linear phase response providing an undistorted ECG signal. FIR filters have the disadvantage of being highly computational. Nearly ideal filter characteristics may be obtained at the price of having to perform many floating point calculations and additions.
A commonly used FIR filter is the Comb Filter. The Comb Filter is a recursive implementation of a non-recursive FIR filter. While offering the advantage of significantly lower computational requirements, this filter offers only moderate attenuation of baseline noise. The maximum stop band attenuation of the Comb Filter is a modest -13.5 db. Another disadvantage of this type of filter is that it has a wide pass band to stop band transition in the frequency domain resulting in poor noise attenuation near the cutoff frequency.
High pass Infinite Impulse Response (IIR) filters are recursive filters that offer the advantage of fewer computation than FIR filters. A problem that results from using high pass IIR filters is the unacceptable level of phase distortion that takes place within the ECG signal. This phase distortion is caused by the nonlinear phase response of IIR filters. A nonlinear phase response results in different frequency components of the signal being delayed or shifted in time by different degrees. For the class of filters appropriate to ECG filtering (Butterworth filters, because of their maximally flat frequency response) the worst distortion occurs at the cutoff frequency of the filter. This results in frequency components Just above the cutoff frequency also being distorted. A solution to the phase distortion problem is to apply the IIR filter to the ECG signal in both directions. This is referred to as a zero phase IIR filter. In a forward direction, using a zero phase IIR filter, the ECG baseline distortions are filtered out but the ECG signal itself is distorted. The reverse direction filtering process corrects the distortion of the ECG signal and further attenuates baseline noise. While correcting phase distortion problems, delay problems make real time implementation of the zero phase IIR filter difficult. Therefore, implementation of a zero phase IIR filter in the exercise stress testing environment is not easily realized because signals must be analyzed and displayed in real time.
As can be seen by the foregoing discussion, there remains a need within the prior art for a filter having a response that enables it to be useful for realtime applications while capable of attenuating frequencies in the 0.67 Hz range or higher without causing phase distortion problems.